Page 1 of 3

THE SEED MONTESSORI SCHOOL Senior High School

COURSE SYLLABUS

Course Title: Precalculus Course Type: Specialized Subject (STEM) Pre-requisite: None Faculty: Louie L. Camral Consultation Hours: TBA Contact Information: louie.camral.tsms@gmail.com Website: www.tsmsmathematics11.weebly.com

Course Description: This specialized subject aims to provide a mathematically sound foundation for senior high school students in the Science, Technology, Engineering and Mathematics strand in preparation for Basic Calculus. Topics that will be covered include conic sections, nonlinear equations, series and mathematical induction, circular and trigonometric functions, and an introduction to the polar coordinate system, harnessing creativity, problem solving, critical thinking and logical reasoning through a highly mathematical approach. Learning Outcomes: Based on the curriculum guide provided by the Department of Education, at the end of the semester, the students should be able to demonstrate competence in the following:

a. model situations and accurately solve problems involving conic sections and systems of nonlinear equations;

b. keenly observe and investigate patterns, formulate appropriate mathematical statements, and prove conjectures using mathematical induction; and

c. formulate and solve accurately situational problems on circular and trigonometric functions Method of Instruction: To achieve the learning outcomes, lessons will be developed and enriched through lecture, classroom discussions, small group activities, mathematical investigations, position papers, problem sets and performance tasks. Technology will be used accordingly to provide visualization and a more thorough understanding. COURSE OUTLINE

WEEK NO.

TOPICS LESSONS ESSENTIAL QUESTIONS

ACTIVITIES / PERFORMANCE

TASKS

1 Fundamentals

of Algebra

a. The Real Number System

b. Properties of Real Numbers

c. Field Axioms d. Properties of Equality

and Inequality

How do math vocabulary and symbols help us effectively think and communicate mathematically?

1-2 Analytic

Geometry

a. Generating Conic Sections

b. Circle Defined c. General Form and

Standard Form of the Equation of a Circle

d. Graphing Circles e. Applications of Circles

How is each conic section related to a double-napped cone? How do you recognize a conic section from a standard form equation?

Conic Project Choices: a. Bridge Project b. Conics in the

Real and Modern World

Page 2 of 3

2-3

f. Parabola Defined g. General Form and

Standard Form of the Equation of a Parabola

h. Graphing Parabolas i. Applications of

Parabolas

How can the understanding of conic sections make more sense of the constructions and designs in our world? What determines the type of conic section you will be using? Why are there key vital coordinates, points and axes and how do they help use and apply the conic section to solve problems?

c. Mathematical Investigation Paper Presentation

Quiz 2

4-5

Analytic Geometry

j. Ellipse Defined k. General Form and

Standard Form of an Ellipse

l. Graphing Ellipses m. Applications of Ellipses

Quiz 3

6-7

n. Hyperbola Defined o. General Form and

Standard Form of a Hyperbola

p. Graphing Hyperbolas q. Applications of

Hyperbolas

7

r. Solving Systems of Nonlinear Equations

s. Applications of Nonlinear Systems

How are nonlinear systems applied in real life?

Conic Art – Creating an art work involving conics using Desmos.

8

Advanced Algebra

a. Recall: Sequences and Series

b. Using the Sigma Notation

c. Proving Identities using Mathematical Induction

d. Special Topic: The Fibonacci Spiral

How are graphing software used in analyzing sequences? Why is proof skill a powerful tool in mathematics? Why is there a need to prove an identity?

Position Paper: Could the Fibonacci Sequence be the “Theory of Everything?” Quiz 4

9

e. Illustrating Triangles in Expanding Binomials

f. Proving and Using the Binomial Theorem

10 MIDTERM EXAMINATION AND INTEGRATION DAY

11

Plane Trigonometry

a. The Unit Circle: Linear and Angular Measures

b. Converting Degree Measures

c. Standard Position and Coterminal Angles

How are circular functions related to trigonometric functions? Why is it not anymore necessary to memorize the function on the unit circle? How can trigonometric identities verified graphically? How are trigonometric identities used in solving trigonometric equations? Why is it necessary to simplify or rewrite a

Modeling Tides – Finding a Trigonometric Function to Model Tides

12-13

d. Using the Circular Functions

e. Graphing Circular Functions

14-15

f. Deriving the Fundamental Trigonometric Identities

g. The Sum and Difference Identities

h. The Double- and Half-Angle Identities

i. Proving Trigonometric Identities

Quiz 5

Page 3 of 3

16-17

j. Inverse Trigonometric Functions

k. Evaluating Inverse Trigonometric Expressions

l. Solving Trigonometric Equations

m. Applications of Trigonometric Equations

trigonometric expression?

Quiz 6

18-19

n. The Polar Coordinate System

o. Converting Polar and Rectangular Coordinates

p. Applications of the Polar Coordinate System

q. Special Topic: Polar Graphs

How similar or different is the polar plane from the rectangular coordinate system?

PolArts – Create an art design using polar graphs through the aid of Desmos Quiz 7

20 FINAL EXAMINATION AND INTEGRATION DAY

Grading System:

COMPONENT PERCENTAGE

Written Work (Quizzes and Problem Sets)

25%

Performance Tasks (Activities, Projects, Position Paper and Write-Ups)

45%

Quarterly Assessment (Midterm Examination or Final Examination)

30%

TOTAL 100%

References:

Barnett, R. A., Ziegler, M. R., Byleen, K. E., & Sobecki, D. (2011). Precalculus (7th ed.). New York,

NY: McGraw-Hill. Fuller, G., & Tarwater, J. D. (1994). Analytic geometry. Reading, MA: Addison-Wesley. Hayden, J. D., & Hall, B. C. (1990). Prentice Hall trigonometry. Englewood Cliffs, NJ: Prentice Hall. Leithold, L. (1989). College algebra and trigonometry. Reading Mass.: Addison-Wesley. Leithold, L. (1997). The calculus 7. New York: Harper Collins College Publ.